A class of solvable non-homogeneous differential operators on the Heisenberg group

Tom 148 / 2001

Detlef Müller, Zhenqiu Zhang Studia Mathematica 148 (2001), 87-96 MSC: 35A05, 43A80. DOI: 10.4064/sm148-1-8


In [8], we studied the problem of local solvability of complex coefficient second order left-invariant differential operators on the Heisenberg group ${\mathbb H}_n$, whose principal parts are “positive combinations of generalized and degenerate generalized sub-Laplacians”, and which are homogeneous under the Heisenberg dilations. In this note, we shall consider the same class of operators, but in the presence of left invariant lower order terms, and shall discuss local solvability for these operators in a complete way. Previously known methods to study such non-homogeneous operators, as in [9] or [6], do not apply to these operators, and it is the main purpose of this article to introduce a new method, which should be applicable also in much wider settings.


  • Detlef MüllerMathematisches Seminar
    Christian-Albrechts-Universität Kiel
    Ludewig-Meyn-Str. 4
    24098 Kiel, Germany
  • Zhenqiu ZhangDepartment of Mathematics
    Tianjin University
    300072 Tianjin, P.R. China

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